In an additive category, given a morphism $f : A\to B$ let $\operatorname{im} f = \ker(\operatorname{coker}(f))$ and $\operatorname{coim} f = \operatorname{coker}(\ker(f))$, if they exist. If they do, then there is a unique morphism $\tilde f$ such that $f = \operatorname{im} f \circ \tilde f \circ \operatorname{coim} f$.

An additive category is "semi-Abelian", if every morphism a has a kernel and cokernel and the $\tilde f$ is mono and epi for all $f$.

I put 'semi-Abelian' in quotation marks because this definition conflicts with the on the nLab, but this definition is given in "Derived Functors in Functional Analysis" by J. Wengenroth (although I don't know who introduced the term originally).

Are "semi-Abelian" categories regular? If not do they have regular epi-mono factorizations?

This might be "obvious", but it isn't to me. Also, I'm also interested in the question with "regular" replaced by "protomodular", but I'm going to postpone that question for now.